| 1 |
#include <triangulate.h>
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| 2 |
#include <math.h>
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| 3 |
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| 4 |
#define CROSS_SINE(v0, v1) ((v0).x * (v1).y - (v1).x * (v0).y)
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| 5 |
#define LENGTH(v0) (sqrt((v0).x * (v0).x + (v0).y * (v0).y))
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| 6 |
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| 7 |
static monchain_t mchain[TRSIZE]; /* Table to hold all the monotone */
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| 8 |
/* polygons . Each monotone polygon */
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| 9 |
/* is a circularly linked list */
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| 10 |
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| 11 |
static vertexchain_t vert[SEGSIZE]; /* chain init. information. This */
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| 12 |
/* is used to decide which */
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| 13 |
/* monotone polygon to split if */
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| 14 |
/* there are several other */
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| 15 |
/* polygons touching at the same */
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| 16 |
/* vertex */
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| 17 |
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| 18 |
static int mon[SEGSIZE]; /* contains position of any vertex in */
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| 19 |
/* the monotone chain for the polygon */
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| 20 |
static int visited[TRSIZE];
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| 21 |
static int chain_idx, op_idx, mon_idx;
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| 22 |
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| 23 |
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| 24 |
static int triangulate_single_polygon(int, int, int, int (*)[3]);
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| 25 |
static int traverse_polygon(int, int, int, int);
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| 26 |
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| 27 |
/* Function returns TRUE if the trapezoid lies inside the polygon */
|
| 28 |
static int inside_polygon(t)
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| 29 |
trap_t *t;
|
| 30 |
{
|
| 31 |
int rseg = t->rseg;
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| 32 |
|
| 33 |
if (t->state == ST_INVALID)
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| 34 |
return 0;
|
| 35 |
|
| 36 |
if ((t->lseg <= 0) || (t->rseg <= 0))
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| 37 |
return 0;
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| 38 |
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| 39 |
if (((t->u0 <= 0) && (t->u1 <= 0)) ||
|
| 40 |
((t->d0 <= 0) && (t->d1 <= 0))) /* triangle */
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| 41 |
return (_greater_than(&seg[rseg].v1, &seg[rseg].v0));
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| 42 |
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| 43 |
return 0;
|
| 44 |
}
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| 45 |
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| 46 |
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| 47 |
/* return a new mon structure from the table */
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| 48 |
static int newmon()
|
| 49 |
{
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| 50 |
return ++mon_idx;
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| 51 |
}
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| 52 |
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| 53 |
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| 54 |
/* return a new chain element from the table */
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| 55 |
static int new_chain_element()
|
| 56 |
{
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| 57 |
return ++chain_idx;
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| 58 |
}
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| 59 |
|
| 60 |
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| 61 |
static double get_angle(vp0, vpnext, vp1)
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| 62 |
point_t *vp0;
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| 63 |
point_t *vpnext;
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| 64 |
point_t *vp1;
|
| 65 |
{
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| 66 |
point_t v0, v1;
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| 67 |
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| 68 |
v0.x = vpnext->x - vp0->x;
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| 69 |
v0.y = vpnext->y - vp0->y;
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| 70 |
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| 71 |
v1.x = vp1->x - vp0->x;
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| 72 |
v1.y = vp1->y - vp0->y;
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| 73 |
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| 74 |
if (CROSS_SINE(v0, v1) >= 0) /* sine is positive */
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| 75 |
return DOT(v0, v1)/LENGTH(v0)/LENGTH(v1);
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| 76 |
else
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| 77 |
return (-1.0 * DOT(v0, v1)/LENGTH(v0)/LENGTH(v1) - 2);
|
| 78 |
}
|
| 79 |
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| 80 |
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| 81 |
/* (v0, v1) is the new diagonal to be added to the polygon. Find which */
|
| 82 |
/* chain to use and return the positions of v0 and v1 in p and q */
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| 83 |
static int get_vertex_positions(v0, v1, ip, iq)
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| 84 |
int v0;
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| 85 |
int v1;
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| 86 |
int *ip;
|
| 87 |
int *iq;
|
| 88 |
{
|
| 89 |
vertexchain_t *vp0, *vp1;
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| 90 |
register int i;
|
| 91 |
double angle, temp;
|
| 92 |
int tp, tq;
|
| 93 |
|
| 94 |
vp0 = &vert[v0];
|
| 95 |
vp1 = &vert[v1];
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| 96 |
|
| 97 |
/* p is identified as follows. Scan from (v0, v1) rightwards till */
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| 98 |
/* you hit the first segment starting from v0. That chain is the */
|
| 99 |
/* chain of our interest */
|
| 100 |
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| 101 |
angle = -4.0;
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| 102 |
for (i = 0; i < 4; i++)
|
| 103 |
{
|
| 104 |
if (vp0->vnext[i] <= 0)
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| 105 |
continue;
|
| 106 |
if ((temp = get_angle(&vp0->pt, &(vert[vp0->vnext[i]].pt),
|
| 107 |
&vp1->pt)) > angle)
|
| 108 |
{
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| 109 |
angle = temp;
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| 110 |
tp = i;
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| 111 |
}
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| 112 |
}
|
| 113 |
|
| 114 |
*ip = tp;
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| 115 |
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| 116 |
/* Do similar actions for q */
|
| 117 |
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| 118 |
angle = -4.0;
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| 119 |
for (i = 0; i < 4; i++)
|
| 120 |
{
|
| 121 |
if (vp1->vnext[i] <= 0)
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| 122 |
continue;
|
| 123 |
if ((temp = get_angle(&vp1->pt, &(vert[vp1->vnext[i]].pt),
|
| 124 |
&vp0->pt)) > angle)
|
| 125 |
{
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| 126 |
angle = temp;
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| 127 |
tq = i;
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| 128 |
}
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| 129 |
}
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| 130 |
|
| 131 |
*iq = tq;
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| 132 |
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| 133 |
return 0;
|
| 134 |
}
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| 135 |
|
| 136 |
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| 137 |
/* v0 and v1 are specified in anti-clockwise order with respect to
|
| 138 |
* the current monotone polygon mcur. Split the current polygon into
|
| 139 |
* two polygons using the diagonal (v0, v1)
|
| 140 |
*/
|
| 141 |
static int make_new_monotone_poly(mcur, v0, v1)
|
| 142 |
int mcur;
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| 143 |
int v0;
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| 144 |
int v1;
|
| 145 |
{
|
| 146 |
int p, q, ip, iq;
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| 147 |
int mnew = newmon();
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| 148 |
int i, j, nf0, nf1;
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| 149 |
vertexchain_t *vp0, *vp1;
|
| 150 |
|
| 151 |
vp0 = &vert[v0];
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| 152 |
vp1 = &vert[v1];
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| 153 |
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| 154 |
get_vertex_positions(v0, v1, &ip, &iq);
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| 155 |
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| 156 |
p = vp0->vpos[ip];
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| 157 |
q = vp1->vpos[iq];
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| 158 |
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| 159 |
/* At this stage, we have got the positions of v0 and v1 in the */
|
| 160 |
/* desired chain. Now modify the linked lists */
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| 161 |
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| 162 |
i = new_chain_element(); /* for the new list */
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| 163 |
j = new_chain_element();
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| 164 |
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| 165 |
mchain[i].vnum = v0;
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| 166 |
mchain[j].vnum = v1;
|
| 167 |
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| 168 |
mchain[i].next = mchain[p].next;
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| 169 |
mchain[mchain[p].next].prev = i;
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| 170 |
mchain[i].prev = j;
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| 171 |
mchain[j].next = i;
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| 172 |
mchain[j].prev = mchain[q].prev;
|
| 173 |
mchain[mchain[q].prev].next = j;
|
| 174 |
|
| 175 |
mchain[p].next = q;
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| 176 |
mchain[q].prev = p;
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| 177 |
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| 178 |
nf0 = vp0->nextfree;
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| 179 |
nf1 = vp1->nextfree;
|
| 180 |
|
| 181 |
vp0->vnext[ip] = v1;
|
| 182 |
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| 183 |
vp0->vpos[nf0] = i;
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| 184 |
vp0->vnext[nf0] = mchain[mchain[i].next].vnum;
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| 185 |
vp1->vpos[nf1] = j;
|
| 186 |
vp1->vnext[nf1] = v0;
|
| 187 |
|
| 188 |
vp0->nextfree++;
|
| 189 |
vp1->nextfree++;
|
| 190 |
|
| 191 |
#ifdef DEBUG
|
| 192 |
fprintf(stderr, "make_poly: mcur = %d, (v0, v1) = (%d, %d)\n",
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| 193 |
mcur, v0, v1);
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| 194 |
fprintf(stderr, "next posns = (p, q) = (%d, %d)\n", p, q);
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| 195 |
#endif
|
| 196 |
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| 197 |
mon[mcur] = p;
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| 198 |
mon[mnew] = i;
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| 199 |
return mnew;
|
| 200 |
}
|
| 201 |
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| 202 |
/* Main routine to get monotone polygons from the trapezoidation of
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| 203 |
* the polygon.
|
| 204 |
*/
|
| 205 |
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| 206 |
int monotonate_trapezoids(n)
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| 207 |
int n;
|
| 208 |
{
|
| 209 |
register int i;
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| 210 |
int tr_start;
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| 211 |
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| 212 |
memset((void *)vert, 0, sizeof(vert));
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| 213 |
memset((void *)visited, 0, sizeof(visited));
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| 214 |
memset((void *)mchain, 0, sizeof(mchain));
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| 215 |
memset((void *)mon, 0, sizeof(mon));
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| 216 |
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| 217 |
/* First locate a trapezoid which lies inside the polygon */
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| 218 |
/* and which is triangular */
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| 219 |
for (i = 0; i < TRSIZE; i++)
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| 220 |
if (inside_polygon(&tr[i]))
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| 221 |
break;
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| 222 |
tr_start = i;
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| 223 |
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| 224 |
/* Initialise the mon data-structure and start spanning all the */
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| 225 |
/* trapezoids within the polygon */
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| 226 |
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| 227 |
#if 0
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| 228 |
for (i = 1; i <= n; i++)
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| 229 |
{
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| 230 |
mchain[i].prev = i - 1;
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| 231 |
mchain[i].next = i + 1;
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| 232 |
mchain[i].vnum = i;
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| 233 |
vert[i].pt = seg[i].v0;
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| 234 |
vert[i].vnext[0] = i + 1; /* next vertex */
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| 235 |
vert[i].vpos[0] = i; /* locn. of next vertex */
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vert[i].nextfree = 1;
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| 237 |
}
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| 238 |
mchain[1].prev = n;
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| 239 |
mchain[n].next = 1;
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| 240 |
vert[n].vnext[0] = 1;
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| 241 |
vert[n].vpos[0] = n;
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| 242 |
chain_idx = n;
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| 243 |
mon_idx = 0;
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| 244 |
mon[0] = 1; /* position of any vertex in the first */
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| 245 |
/* chain */
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| 246 |
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| 247 |
#else
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| 248 |
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| 249 |
for (i = 1; i <= n; i++)
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| 250 |
{
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| 251 |
mchain[i].prev = seg[i].prev;
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| 252 |
mchain[i].next = seg[i].next;
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| 253 |
mchain[i].vnum = i;
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| 254 |
vert[i].pt = seg[i].v0;
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| 255 |
vert[i].vnext[0] = seg[i].next; /* next vertex */
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| 256 |
vert[i].vpos[0] = i; /* locn. of next vertex */
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| 257 |
vert[i].nextfree = 1;
|
| 258 |
}
|
| 259 |
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| 260 |
chain_idx = n;
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| 261 |
mon_idx = 0;
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| 262 |
mon[0] = 1; /* position of any vertex in the first */
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| 263 |
/* chain */
|
| 264 |
|
| 265 |
#endif
|
| 266 |
|
| 267 |
/* traverse the polygon */
|
| 268 |
if (tr[tr_start].u0 > 0)
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| 269 |
traverse_polygon(0, tr_start, tr[tr_start].u0, TR_FROM_UP);
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| 270 |
else if (tr[tr_start].d0 > 0)
|
| 271 |
traverse_polygon(0, tr_start, tr[tr_start].d0, TR_FROM_DN);
|
| 272 |
|
| 273 |
/* return the number of polygons created */
|
| 274 |
return newmon();
|
| 275 |
}
|
| 276 |
|
| 277 |
|
| 278 |
/* recursively visit all the trapezoids */
|
| 279 |
static int traverse_polygon(mcur, trnum, from, dir)
|
| 280 |
int mcur;
|
| 281 |
int trnum;
|
| 282 |
int from;
|
| 283 |
int dir;
|
| 284 |
{
|
| 285 |
trap_t *t = &tr[trnum];
|
| 286 |
int howsplit, mnew;
|
| 287 |
int v0, v1, v0next, v1next;
|
| 288 |
int retval, tmp;
|
| 289 |
int do_switch = FALSE;
|
| 290 |
|
| 291 |
if ((trnum <= 0) || visited[trnum])
|
| 292 |
return 0;
|
| 293 |
|
| 294 |
visited[trnum] = TRUE;
|
| 295 |
|
| 296 |
/* We have much more information available here. */
|
| 297 |
/* rseg: goes upwards */
|
| 298 |
/* lseg: goes downwards */
|
| 299 |
|
| 300 |
/* Initially assume that dir = TR_FROM_DN (from the left) */
|
| 301 |
/* Switch v0 and v1 if necessary afterwards */
|
| 302 |
|
| 303 |
|
| 304 |
/* special cases for triangles with cusps at the opposite ends. */
|
| 305 |
/* take care of this first */
|
| 306 |
if ((t->u0 <= 0) && (t->u1 <= 0))
|
| 307 |
{
|
| 308 |
if ((t->d0 > 0) && (t->d1 > 0)) /* downward opening triangle */
|
| 309 |
{
|
| 310 |
v0 = tr[t->d1].lseg;
|
| 311 |
v1 = t->lseg;
|
| 312 |
if (from == t->d1)
|
| 313 |
{
|
| 314 |
do_switch = TRUE;
|
| 315 |
mnew = make_new_monotone_poly(mcur, v1, v0);
|
| 316 |
traverse_polygon(mcur, t->d1, trnum, TR_FROM_UP);
|
| 317 |
traverse_polygon(mnew, t->d0, trnum, TR_FROM_UP);
|
| 318 |
}
|
| 319 |
else
|
| 320 |
{
|
| 321 |
mnew = make_new_monotone_poly(mcur, v0, v1);
|
| 322 |
traverse_polygon(mcur, t->d0, trnum, TR_FROM_UP);
|
| 323 |
traverse_polygon(mnew, t->d1, trnum, TR_FROM_UP);
|
| 324 |
}
|
| 325 |
}
|
| 326 |
else
|
| 327 |
{
|
| 328 |
retval = SP_NOSPLIT; /* Just traverse all neighbours */
|
| 329 |
traverse_polygon(mcur, t->u0, trnum, TR_FROM_DN);
|
| 330 |
traverse_polygon(mcur, t->u1, trnum, TR_FROM_DN);
|
| 331 |
traverse_polygon(mcur, t->d0, trnum, TR_FROM_UP);
|
| 332 |
traverse_polygon(mcur, t->d1, trnum, TR_FROM_UP);
|
| 333 |
}
|
| 334 |
}
|
| 335 |
|
| 336 |
else if ((t->d0 <= 0) && (t->d1 <= 0))
|
| 337 |
{
|
| 338 |
if ((t->u0 > 0) && (t->u1 > 0)) /* upward opening triangle */
|
| 339 |
{
|
| 340 |
v0 = t->rseg;
|
| 341 |
v1 = tr[t->u0].rseg;
|
| 342 |
if (from == t->u1)
|
| 343 |
{
|
| 344 |
do_switch = TRUE;
|
| 345 |
mnew = make_new_monotone_poly(mcur, v1, v0);
|
| 346 |
traverse_polygon(mcur, t->u1, trnum, TR_FROM_DN);
|
| 347 |
traverse_polygon(mnew, t->u0, trnum, TR_FROM_DN);
|
| 348 |
}
|
| 349 |
else
|
| 350 |
{
|
| 351 |
mnew = make_new_monotone_poly(mcur, v0, v1);
|
| 352 |
traverse_polygon(mcur, t->u0, trnum, TR_FROM_DN);
|
| 353 |
traverse_polygon(mnew, t->u1, trnum, TR_FROM_DN);
|
| 354 |
}
|
| 355 |
}
|
| 356 |
else
|
| 357 |
{
|
| 358 |
retval = SP_NOSPLIT; /* Just traverse all neighbours */
|
| 359 |
traverse_polygon(mcur, t->u0, trnum, TR_FROM_DN);
|
| 360 |
traverse_polygon(mcur, t->u1, trnum, TR_FROM_DN);
|
| 361 |
traverse_polygon(mcur, t->d0, trnum, TR_FROM_UP);
|
| 362 |
traverse_polygon(mcur, t->d1, trnum, TR_FROM_UP);
|
| 363 |
}
|
| 364 |
}
|
| 365 |
|
| 366 |
else if ((t->u0 > 0) && (t->u1 > 0))
|
| 367 |
{
|
| 368 |
if ((t->d0 > 0) && (t->d1 > 0)) /* downward + upward cusps */
|
| 369 |
{
|
| 370 |
v0 = tr[t->d1].lseg;
|
| 371 |
v1 = tr[t->u0].rseg;
|
| 372 |
retval = SP_2UP_2DN;
|
| 373 |
if (((dir == TR_FROM_DN) && (t->d1 == from)) ||
|
| 374 |
((dir == TR_FROM_UP) && (t->u1 == from)))
|
| 375 |
{
|
| 376 |
do_switch = TRUE;
|
| 377 |
mnew = make_new_monotone_poly(mcur, v1, v0);
|
| 378 |
traverse_polygon(mcur, t->u1, trnum, TR_FROM_DN);
|
| 379 |
traverse_polygon(mcur, t->d1, trnum, TR_FROM_UP);
|
| 380 |
traverse_polygon(mnew, t->u0, trnum, TR_FROM_DN);
|
| 381 |
traverse_polygon(mnew, t->d0, trnum, TR_FROM_UP);
|
| 382 |
}
|
| 383 |
else
|
| 384 |
{
|
| 385 |
mnew = make_new_monotone_poly(mcur, v0, v1);
|
| 386 |
traverse_polygon(mcur, t->u0, trnum, TR_FROM_DN);
|
| 387 |
traverse_polygon(mcur, t->d0, trnum, TR_FROM_UP);
|
| 388 |
traverse_polygon(mnew, t->u1, trnum, TR_FROM_DN);
|
| 389 |
traverse_polygon(mnew, t->d1, trnum, TR_FROM_UP);
|
| 390 |
}
|
| 391 |
}
|
| 392 |
else /* only downward cusp */
|
| 393 |
{
|
| 394 |
if (_equal_to(&t->lo, &seg[t->lseg].v1))
|
| 395 |
{
|
| 396 |
v0 = tr[t->u0].rseg;
|
| 397 |
v1 = seg[t->lseg].next;
|
| 398 |
|
| 399 |
retval = SP_2UP_LEFT;
|
| 400 |
if ((dir == TR_FROM_UP) && (t->u0 == from))
|
| 401 |
{
|
| 402 |
do_switch = TRUE;
|
| 403 |
mnew = make_new_monotone_poly(mcur, v1, v0);
|
| 404 |
traverse_polygon(mcur, t->u0, trnum, TR_FROM_DN);
|
| 405 |
traverse_polygon(mnew, t->d0, trnum, TR_FROM_UP);
|
| 406 |
traverse_polygon(mnew, t->u1, trnum, TR_FROM_DN);
|
| 407 |
traverse_polygon(mnew, t->d1, trnum, TR_FROM_UP);
|
| 408 |
}
|
| 409 |
else
|
| 410 |
{
|
| 411 |
mnew = make_new_monotone_poly(mcur, v0, v1);
|
| 412 |
traverse_polygon(mcur, t->u1, trnum, TR_FROM_DN);
|
| 413 |
traverse_polygon(mcur, t->d0, trnum, TR_FROM_UP);
|
| 414 |
traverse_polygon(mcur, t->d1, trnum, TR_FROM_UP);
|
| 415 |
traverse_polygon(mnew, t->u0, trnum, TR_FROM_DN);
|
| 416 |
}
|
| 417 |
}
|
| 418 |
else
|
| 419 |
{
|
| 420 |
v0 = t->rseg;
|
| 421 |
v1 = tr[t->u0].rseg;
|
| 422 |
retval = SP_2UP_RIGHT;
|
| 423 |
if ((dir == TR_FROM_UP) && (t->u1 == from))
|
| 424 |
{
|
| 425 |
do_switch = TRUE;
|
| 426 |
mnew = make_new_monotone_poly(mcur, v1, v0);
|
| 427 |
traverse_polygon(mcur, t->u1, trnum, TR_FROM_DN);
|
| 428 |
traverse_polygon(mnew, t->d1, trnum, TR_FROM_UP);
|
| 429 |
traverse_polygon(mnew, t->d0, trnum, TR_FROM_UP);
|
| 430 |
traverse_polygon(mnew, t->u0, trnum, TR_FROM_DN);
|
| 431 |
}
|
| 432 |
else
|
| 433 |
{
|
| 434 |
mnew = make_new_monotone_poly(mcur, v0, v1);
|
| 435 |
traverse_polygon(mcur, t->u0, trnum, TR_FROM_DN);
|
| 436 |
traverse_polygon(mcur, t->d0, trnum, TR_FROM_UP);
|
| 437 |
traverse_polygon(mcur, t->d1, trnum, TR_FROM_UP);
|
| 438 |
traverse_polygon(mnew, t->u1, trnum, TR_FROM_DN);
|
| 439 |
}
|
| 440 |
}
|
| 441 |
}
|
| 442 |
}
|
| 443 |
else if ((t->u0 > 0) || (t->u1 > 0)) /* no downward cusp */
|
| 444 |
{
|
| 445 |
if ((t->d0 > 0) && (t->d1 > 0)) /* only upward cusp */
|
| 446 |
{
|
| 447 |
if (_equal_to(&t->hi, &seg[t->lseg].v0))
|
| 448 |
{
|
| 449 |
v0 = tr[t->d1].lseg;
|
| 450 |
v1 = t->lseg;
|
| 451 |
retval = SP_2DN_LEFT;
|
| 452 |
if (!((dir == TR_FROM_DN) && (t->d0 == from)))
|
| 453 |
{
|
| 454 |
do_switch = TRUE;
|
| 455 |
mnew = make_new_monotone_poly(mcur, v1, v0);
|
| 456 |
traverse_polygon(mcur, t->u1, trnum, TR_FROM_DN);
|
| 457 |
traverse_polygon(mcur, t->d1, trnum, TR_FROM_UP);
|
| 458 |
traverse_polygon(mcur, t->u0, trnum, TR_FROM_DN);
|
| 459 |
traverse_polygon(mnew, t->d0, trnum, TR_FROM_UP);
|
| 460 |
}
|
| 461 |
else
|
| 462 |
{
|
| 463 |
mnew = make_new_monotone_poly(mcur, v0, v1);
|
| 464 |
traverse_polygon(mcur, t->d0, trnum, TR_FROM_UP);
|
| 465 |
traverse_polygon(mnew, t->u0, trnum, TR_FROM_DN);
|
| 466 |
traverse_polygon(mnew, t->u1, trnum, TR_FROM_DN);
|
| 467 |
traverse_polygon(mnew, t->d1, trnum, TR_FROM_UP);
|
| 468 |
}
|
| 469 |
}
|
| 470 |
else
|
| 471 |
{
|
| 472 |
v0 = tr[t->d1].lseg;
|
| 473 |
v1 = seg[t->rseg].next;
|
| 474 |
|
| 475 |
retval = SP_2DN_RIGHT;
|
| 476 |
if ((dir == TR_FROM_DN) && (t->d1 == from))
|
| 477 |
{
|
| 478 |
do_switch = TRUE;
|
| 479 |
mnew = make_new_monotone_poly(mcur, v1, v0);
|
| 480 |
traverse_polygon(mcur, t->d1, trnum, TR_FROM_UP);
|
| 481 |
traverse_polygon(mnew, t->u1, trnum, TR_FROM_DN);
|
| 482 |
traverse_polygon(mnew, t->u0, trnum, TR_FROM_DN);
|
| 483 |
traverse_polygon(mnew, t->d0, trnum, TR_FROM_UP);
|
| 484 |
}
|
| 485 |
else
|
| 486 |
{
|
| 487 |
mnew = make_new_monotone_poly(mcur, v0, v1);
|
| 488 |
traverse_polygon(mcur, t->u0, trnum, TR_FROM_DN);
|
| 489 |
traverse_polygon(mcur, t->d0, trnum, TR_FROM_UP);
|
| 490 |
traverse_polygon(mcur, t->u1, trnum, TR_FROM_DN);
|
| 491 |
traverse_polygon(mnew, t->d1, trnum, TR_FROM_UP);
|
| 492 |
}
|
| 493 |
}
|
| 494 |
}
|
| 495 |
else /* no cusp */
|
| 496 |
{
|
| 497 |
if (_equal_to(&t->hi, &seg[t->lseg].v0) &&
|
| 498 |
_equal_to(&t->lo, &seg[t->rseg].v0))
|
| 499 |
{
|
| 500 |
v0 = t->rseg;
|
| 501 |
v1 = t->lseg;
|
| 502 |
retval = SP_SIMPLE_LRDN;
|
| 503 |
if (dir == TR_FROM_UP)
|
| 504 |
{
|
| 505 |
do_switch = TRUE;
|
| 506 |
mnew = make_new_monotone_poly(mcur, v1, v0);
|
| 507 |
traverse_polygon(mcur, t->u0, trnum, TR_FROM_DN);
|
| 508 |
traverse_polygon(mcur, t->u1, trnum, TR_FROM_DN);
|
| 509 |
traverse_polygon(mnew, t->d1, trnum, TR_FROM_UP);
|
| 510 |
traverse_polygon(mnew, t->d0, trnum, TR_FROM_UP);
|
| 511 |
}
|
| 512 |
else
|
| 513 |
{
|
| 514 |
mnew = make_new_monotone_poly(mcur, v0, v1);
|
| 515 |
traverse_polygon(mcur, t->d1, trnum, TR_FROM_UP);
|
| 516 |
traverse_polygon(mcur, t->d0, trnum, TR_FROM_UP);
|
| 517 |
traverse_polygon(mnew, t->u0, trnum, TR_FROM_DN);
|
| 518 |
traverse_polygon(mnew, t->u1, trnum, TR_FROM_DN);
|
| 519 |
}
|
| 520 |
}
|
| 521 |
else if (_equal_to(&t->hi, &seg[t->rseg].v1) &&
|
| 522 |
_equal_to(&t->lo, &seg[t->lseg].v1))
|
| 523 |
{
|
| 524 |
v0 = seg[t->rseg].next;
|
| 525 |
v1 = seg[t->lseg].next;
|
| 526 |
|
| 527 |
retval = SP_SIMPLE_LRUP;
|
| 528 |
if (dir == TR_FROM_UP)
|
| 529 |
{
|
| 530 |
do_switch = TRUE;
|
| 531 |
mnew = make_new_monotone_poly(mcur, v1, v0);
|
| 532 |
traverse_polygon(mcur, t->u0, trnum, TR_FROM_DN);
|
| 533 |
traverse_polygon(mcur, t->u1, trnum, TR_FROM_DN);
|
| 534 |
traverse_polygon(mnew, t->d1, trnum, TR_FROM_UP);
|
| 535 |
traverse_polygon(mnew, t->d0, trnum, TR_FROM_UP);
|
| 536 |
}
|
| 537 |
else
|
| 538 |
{
|
| 539 |
mnew = make_new_monotone_poly(mcur, v0, v1);
|
| 540 |
traverse_polygon(mcur, t->d1, trnum, TR_FROM_UP);
|
| 541 |
traverse_polygon(mcur, t->d0, trnum, TR_FROM_UP);
|
| 542 |
traverse_polygon(mnew, t->u0, trnum, TR_FROM_DN);
|
| 543 |
traverse_polygon(mnew, t->u1, trnum, TR_FROM_DN);
|
| 544 |
}
|
| 545 |
}
|
| 546 |
else /* no split possible */
|
| 547 |
{
|
| 548 |
retval = SP_NOSPLIT;
|
| 549 |
traverse_polygon(mcur, t->u0, trnum, TR_FROM_DN);
|
| 550 |
traverse_polygon(mcur, t->d0, trnum, TR_FROM_UP);
|
| 551 |
traverse_polygon(mcur, t->u1, trnum, TR_FROM_DN);
|
| 552 |
traverse_polygon(mcur, t->d1, trnum, TR_FROM_UP);
|
| 553 |
}
|
| 554 |
}
|
| 555 |
}
|
| 556 |
|
| 557 |
return retval;
|
| 558 |
}
|
| 559 |
|
| 560 |
|
| 561 |
/* For each monotone polygon, find the ymax and ymin (to determine the */
|
| 562 |
/* two y-monotone chains) and pass on this monotone polygon for greedy */
|
| 563 |
/* triangulation. */
|
| 564 |
/* Take care not to triangulate duplicate monotone polygons */
|
| 565 |
|
| 566 |
int triangulate_monotone_polygons(nvert, nmonpoly, op)
|
| 567 |
int nvert;
|
| 568 |
int nmonpoly;
|
| 569 |
int op[][3];
|
| 570 |
{
|
| 571 |
register int i;
|
| 572 |
point_t ymax, ymin;
|
| 573 |
int p, vfirst, posmax, posmin, v;
|
| 574 |
int vcount, processed;
|
| 575 |
|
| 576 |
#ifdef DEBUG
|
| 577 |
for (i = 0; i < nmonpoly; i++)
|
| 578 |
{
|
| 579 |
fprintf(stderr, "\n\nPolygon %d: ", i);
|
| 580 |
vfirst = mchain[mon[i]].vnum;
|
| 581 |
p = mchain[mon[i]].next;
|
| 582 |
fprintf (stderr, "%d ", mchain[mon[i]].vnum);
|
| 583 |
while (mchain[p].vnum != vfirst)
|
| 584 |
{
|
| 585 |
fprintf(stderr, "%d ", mchain[p].vnum);
|
| 586 |
p = mchain[p].next;
|
| 587 |
}
|
| 588 |
}
|
| 589 |
fprintf(stderr, "\n");
|
| 590 |
#endif
|
| 591 |
|
| 592 |
op_idx = 0;
|
| 593 |
for (i = 0; i < nmonpoly; i++)
|
| 594 |
{
|
| 595 |
vcount = 1;
|
| 596 |
processed = FALSE;
|
| 597 |
vfirst = mchain[mon[i]].vnum;
|
| 598 |
ymax = ymin = vert[vfirst].pt;
|
| 599 |
posmax = posmin = mon[i];
|
| 600 |
mchain[mon[i]].marked = TRUE;
|
| 601 |
p = mchain[mon[i]].next;
|
| 602 |
while ((v = mchain[p].vnum) != vfirst)
|
| 603 |
{
|
| 604 |
if (mchain[p].marked)
|
| 605 |
{
|
| 606 |
processed = TRUE;
|
| 607 |
break; /* break from while */
|
| 608 |
}
|
| 609 |
else
|
| 610 |
mchain[p].marked = TRUE;
|
| 611 |
|
| 612 |
if (_greater_than(&vert[v].pt, &ymax))
|
| 613 |
{
|
| 614 |
ymax = vert[v].pt;
|
| 615 |
posmax = p;
|
| 616 |
}
|
| 617 |
if (_less_than(&vert[v].pt, &ymin))
|
| 618 |
{
|
| 619 |
ymin = vert[v].pt;
|
| 620 |
posmin = p;
|
| 621 |
}
|
| 622 |
p = mchain[p].next;
|
| 623 |
vcount++;
|
| 624 |
}
|
| 625 |
|
| 626 |
if (processed) /* Go to next polygon */
|
| 627 |
continue;
|
| 628 |
|
| 629 |
if (vcount == 3) /* already a triangle */
|
| 630 |
{
|
| 631 |
op[op_idx][0] = mchain[p].vnum;
|
| 632 |
op[op_idx][1] = mchain[mchain[p].next].vnum;
|
| 633 |
op[op_idx][2] = mchain[mchain[p].prev].vnum;
|
| 634 |
op_idx++;
|
| 635 |
}
|
| 636 |
else /* triangulate the polygon */
|
| 637 |
{
|
| 638 |
v = mchain[mchain[posmax].next].vnum;
|
| 639 |
if (_equal_to(&vert[v].pt, &ymin))
|
| 640 |
{ /* LHS is a single line */
|
| 641 |
triangulate_single_polygon(nvert, posmax, TRI_LHS, op);
|
| 642 |
}
|
| 643 |
else
|
| 644 |
triangulate_single_polygon(nvert, posmax, TRI_RHS, op);
|
| 645 |
}
|
| 646 |
}
|
| 647 |
|
| 648 |
#ifdef DEBUG
|
| 649 |
for (i = 0; i < op_idx; i++)
|
| 650 |
fprintf(stderr, "tri #%d: (%d, %d, %d)\n", i, op[i][0], op[i][1],
|
| 651 |
op[i][2]);
|
| 652 |
#endif
|
| 653 |
return op_idx;
|
| 654 |
}
|
| 655 |
|
| 656 |
|
| 657 |
/* A greedy corner-cutting algorithm to triangulate a y-monotone
|
| 658 |
* polygon in O(n) time.
|
| 659 |
* Joseph O-Rourke, Computational Geometry in C.
|
| 660 |
*/
|
| 661 |
static int triangulate_single_polygon(nvert, posmax, side, op)
|
| 662 |
int nvert;
|
| 663 |
int posmax;
|
| 664 |
int side;
|
| 665 |
int op[][3];
|
| 666 |
{
|
| 667 |
register int v;
|
| 668 |
int rc[SEGSIZE], ri = 0; /* reflex chain */
|
| 669 |
int endv, tmp, vpos;
|
| 670 |
|
| 671 |
if (side == TRI_RHS) /* RHS segment is a single segment */
|
| 672 |
{
|
| 673 |
rc[0] = mchain[posmax].vnum;
|
| 674 |
tmp = mchain[posmax].next;
|
| 675 |
rc[1] = mchain[tmp].vnum;
|
| 676 |
ri = 1;
|
| 677 |
|
| 678 |
vpos = mchain[tmp].next;
|
| 679 |
v = mchain[vpos].vnum;
|
| 680 |
|
| 681 |
if ((endv = mchain[mchain[posmax].prev].vnum) == 0)
|
| 682 |
endv = nvert;
|
| 683 |
}
|
| 684 |
else /* LHS is a single segment */
|
| 685 |
{
|
| 686 |
tmp = mchain[posmax].next;
|
| 687 |
rc[0] = mchain[tmp].vnum;
|
| 688 |
tmp = mchain[tmp].next;
|
| 689 |
rc[1] = mchain[tmp].vnum;
|
| 690 |
ri = 1;
|
| 691 |
|
| 692 |
vpos = mchain[tmp].next;
|
| 693 |
v = mchain[vpos].vnum;
|
| 694 |
|
| 695 |
endv = mchain[posmax].vnum;
|
| 696 |
}
|
| 697 |
|
| 698 |
while ((v != endv) || (ri > 1))
|
| 699 |
{
|
| 700 |
if (ri > 0) /* reflex chain is non-empty */
|
| 701 |
{
|
| 702 |
if (CROSS(vert[v].pt, vert[rc[ri - 1]].pt,
|
| 703 |
vert[rc[ri]].pt) > 0)
|
| 704 |
{ /* convex corner: cut if off */
|
| 705 |
op[op_idx][0] = rc[ri - 1];
|
| 706 |
op[op_idx][1] = rc[ri];
|
| 707 |
op[op_idx][2] = v;
|
| 708 |
op_idx++;
|
| 709 |
ri--;
|
| 710 |
}
|
| 711 |
else /* non-convex */
|
| 712 |
{ /* add v to the chain */
|
| 713 |
ri++;
|
| 714 |
rc[ri] = v;
|
| 715 |
vpos = mchain[vpos].next;
|
| 716 |
v = mchain[vpos].vnum;
|
| 717 |
}
|
| 718 |
}
|
| 719 |
else /* reflex-chain empty: add v to the */
|
| 720 |
{ /* reflex chain and advance it */
|
| 721 |
rc[++ri] = v;
|
| 722 |
vpos = mchain[vpos].next;
|
| 723 |
v = mchain[vpos].vnum;
|
| 724 |
}
|
| 725 |
} /* end-while */
|
| 726 |
|
| 727 |
/* reached the bottom vertex. Add in the triangle formed */
|
| 728 |
op[op_idx][0] = rc[ri - 1];
|
| 729 |
op[op_idx][1] = rc[ri];
|
| 730 |
op[op_idx][2] = v;
|
| 731 |
op_idx++;
|
| 732 |
ri--;
|
| 733 |
|
| 734 |
return 0;
|
| 735 |
}
|
| 736 |
|
| 737 |
|
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